Question

Q1.Find the coordinates of the point which divides the line segment joining the points (4, – 3) and (8,5) in the ratio 2:1 internally.

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Answer 1

Step-by-step explanation:

Answer:

The formula to find the coordinates of Point of Division, when line is divided internally, is given as:

$\boxed{ \bf{ (x, y) = [\dfrac{ mx_2 + nx_1}{m+n}\:,\: \dfrac{my_2 + ny_1}{m+n}]}} </p><p>$

According to the question,

x₁ = 4, y₁ = -3

x₂ = 8, y₂ = 5

m : n = ( 2 : 1 )

Substituting the values we get:

$\begin{gathered}\implies x-coordinate = \dfrac{ mx_2 + nx_1}{m+n}\\\\\\\implies x= \dfrac{ 2(8) + 1(4)}{2+1}\\\\\\\implies \boxed{ \bf{ x = \dfrac{20}{3}}}\end{gathered}$

Similarly,

$\begin{gathered}\implies y-coordinate = \dfrac{my_2 + ny_1}{m+n}\\\\\\\implies y = \dfrac{ 2(5) + 1(-3) }{2 + 1 }\\\\\\\implies \boxed{ \bf{ y = \dfrac{7}{3}}}\end{gathered}$

The co-ordinate of point C will be (7,3) .